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A054735
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Sum of twin prime pairs.
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16
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8, 12, 24, 36, 60, 84, 120, 144, 204, 216, 276, 300, 360, 384, 396, 456, 480, 540, 564, 624, 696, 840, 864, 924, 1044, 1140, 1200, 1236, 1284, 1320, 1620, 1644, 1656, 1716, 1764, 2040, 2064, 2100, 2124, 2184, 2304, 2460, 2556, 2580, 2604, 2640, 2856, 2904
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| (p^q)+(q^p) calculated modulo pq, where (p,q) is the n-th twin prime pair. Example: (599^601)+(601^599) == 1200 mod (599*601). - Sam Alexander (amnalexander(AT)yahoo.com), Nov 14 2003
El'hakk makes the following claim (without any proof): (q^p)+(p^q) = 2*cosh(q arctanh( sqrt( 1-((2/p)^2) ) )) + 2cosh(p arctanh( sqrt( 1-((2/q)^2) ) )) mod p*q - Sam Alexander (amnalexander(AT)yahoo.com), Nov 14 2003
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LINKS
| El'hakk, Page of the time traveler
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FORMULA
| a(n) = 2*A014574(n) = 4*A040040(n) = A111046(n)/2.
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EXAMPLE
| a(3)=24 because the twin primes 11 and 13 add to 24.
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MAPLE
| ZL:=[]:for p from 1 to 1451 do if (isprime(p) and isprime(p+2)) then ZL:=[op(ZL), p+(p+2)]; fi; od; print(ZL); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 07 2007
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MATHEMATICA
| Select[Table[Prime[n] + 1, {n, 230}], PrimeQ[ # + 1] &] *2 - Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 12 2005
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CROSSREFS
| Cf. A001359, A006512, A014574, A040040, A111046.
Sequence in context: A105571 A141616 A088525 * A162691 A077566 A067677
Adjacent sequences: A054732 A054733 A054734 * A054736 A054737 A054738
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KEYWORD
| easy,nonn
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AUTHOR
| Enoch Haga (Enokh(AT)comcast.net), Apr 22 2000
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EXTENSIONS
| Additional comments from Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 16 2003
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